The Ford family maintains effective control over the automaker through ownership of a separate class of stock. The shares gives them 40% of voting power, an arrangement that has been criticized in recent years.

Musk's dig at Ford(F) comes after Tesla surpassed it in market value last week. This week, Tesla(TSLA) briefly became the most valuable carmaker in America when it overtook GM for a while.

Reuters reported that the investor group also wants Tesla's directors to be re-elected each year.

"We expect that as companies make the transition to publicly-traded status, the governance structures and practices in place at the time of the IPO will evolve to align with the company's changing strategy," Reuters cited the letter as saying. "However, Tesla's seven-member board is largely unchanged from its pre-IPO days."

Tesla went public in 2010.

@Reuters This investor group should buy Ford stock. Their governance is amazing ...

The investor letter had five signatories, Reuters reported, including the California State Teachers Retirement System, Hermes Equity Ownership Services and CtW Investment Group. Those three didn't respond to requests for comment.

Tesla doesn't sell nearly as many cars as major automakers such as Ford and GM. But investors seem excited about Tesla's upcoming Model 3 car, which could help make Tesla a more mainstream auto company instead of just a luxury electric car maker.